SUPPLEMENTAL MATERIAL
for
A FRESH LOOK AT DENSE HYDROGEN UNDER PRESSURE:
1. An introduction to the problem, and an index probing
equalization of H-H distances
Vanessa Labet,1 Paulina Gonzalez-Morelos,1 Roald Hoffmann,1 N. W. Ashcroft2
1
Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca,
NY, 14853, USA
2
Laboratory of Atomic and Solid State Physics and Cornell Center for Materials Research,
Cornell University, Clark Hall, Ithaca, NY, 14853, USA
S1
Figure S1. Different views of the P63/m structure at P=300GPa (rs = 1.33 – a relative
compression of 12.6). (a: along axis a; b: along axis b; c: along axis c; d: one layer). The
dashed lines represent the unit cell. At this pressure, the interlayer distance, defined as the
shortest distance between two successive (ab) planes containing H2 units, is 1.63Å (3.09 a0).
S2
Figure S2. Different views of the C2/c structure at P=300GPa (rs = 1.33 – a relative
compression of 12.6). (a: along axis a; b: along axis b; c: along axis c; d: one layer). The
dashed lines represent the unit cell. At this pressure, the interlayer distance, defined as the
shortest distance between two successive (ab) planes containing H2 units, is 1.26Å (2.37 a0).
S3
Figure S3. Different views of the Cmca-12 structure at P=300GPa (rs = 1.33 – a relative
compression of 12.6). (a: along axis a; b: along axis b; c: along axis c; d: one layer). The
dashed lines represent the unit cell. At this pressure, the interlayer distance, defined as the
shortest distance between two successive (bc) planes containing H2 units, is 1.28Å (2.42 a0).
S4
Figure S4. Different views of the Cmca structure at P=300GPa (rs = 1.33 – a relative
compression of 12.6). (a: along axis a; b: along axis b; c: along axis c; d: one layer). The
dashed lines represent the unit cell. At that pressure, the interlayer distance, defined as the
shortest distance between two successive (bc) planes containing H2 units, is 0.82Å (1.55 a0). The
shortest intermolecular H-H separation connects protons which are in two different layers,
which is an indication that this structure actually cannot be described as layered.
S5
Figure S5. Different views of the I41/amd structure at P=500GPa (rs = 1.24 – a relative
compression of 15.8). (a: along axis a; b: along axis b; c: along axis c). The dashed rectangles
represent the unit cell.
S6
Figure S6. Evolution with pressure of the interlayer (empty circles) and average second shortest
H-H distances (full squares) in the P63/m, C2/c, Cmca-12 and Cmca structures. The interlayer
distance is defined as the distance between two layers of H2 molecules. Practically, it was
evaluated by dividing the length of the unit cell vector perpendicular to the H2 layers by the
number of layers in the unit cell. In the P63/m and Cmca structures, the second shortest H-H
distance involves H2 molecules belonging to two different layers, that’s why the interlayer
distance is shorter than the shortest intermolecular distance. On the contrary, in the C2/c and
Cmca-12 structures, the second shortest H-H distance involves H2 molecules of the same layer.
S7
Figure S7. Evolution of the intramolecular H-H distance under pressure. Black squares and red
circles come from Refs. 46 and 45, respectively, and are deduced from experimental roton
spectra. The points with blue triangles come from our computations of the P63/m and C2/c
structures for hydrogen.
S8